So why not make it the same day for each state to hold their primaries? I think the voting is skewed when a state or several states that are more liberal or more conservative gets to go first. Thus sealing up the outcome before the other states have a chance down the line.
Sounds good to me because with such a system, people in the various states, knowing that the whole country is voting would mitigate the degree to which they might vote for a candidate based mostly on local factors. This would force them to think about the good of the country as a whole.